@Donnia0 As a homeowner, I can tell you that I would never let anyone rent my house and then turn around and list it on a booking site. And if I found out they were doing it without my knowledge, I would be livid and evict them immediately. Tenants (that would be you in this case) have no financial stake in a home they don't own. What if the airbnb guests break the washing machine- are you going to be okay with paying for the repairs, or buying a new machine? They plug up the toilet, you going to call the plumber and pay out of your pocket, or you going to call the landlord and say the toilet needs repair and expect him to fix it?
Perhaps you're a very responsible person and would, in fact, take on those costs yourself and you seem responsible just by the fact that you asked here about how to present it to a homeowner. But it's really a lot to ask that a homeowner not only trust you to look after the place if you are living in it, but to trust that you would be knowledgeable about knowing how to vet airbnb guests and deal with any damage they cause.
You may be able to find landlords who would be okay with this, I can only speak for myself.